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Simplifying -36.01 + -2x + -0.001x2 = 0 Solving -36.01 + -2x + -0.001x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.001 the coefficient of the squared term: Divide each side by '-0.001'. 36010 + 2000x + x2 = 0 Move the constant term to the right: Add '-36010' to each side of the equation. 36010 + 2000x + -36010 + x2 = 0 + -36010 Reorder the terms: 36010 + -36010 + 2000x + x2 = 0 + -36010 Combine like terms: 36010 + -36010 = 0 0 + 2000x + x2 = 0 + -36010 2000x + x2 = 0 + -36010 Combine like terms: 0 + -36010 = -36010 2000x + x2 = -36010 The x term is 2000x. Take half its coefficient (1000). Square it (1000000) and add it to both sides. Add '1000000' to each side of the equation. 2000x + 1000000 + x2 = -36010 + 1000000 Reorder the terms: 1000000 + 2000x + x2 = -36010 + 1000000 Combine like terms: -36010 + 1000000 = 963990 1000000 + 2000x + x2 = 963990 Factor a perfect square on the left side: (x + 1000)(x + 1000) = 963990 Calculate the square root of the right side: 981.829924172 Break this problem into two subproblems by setting (x + 1000) equal to 981.829924172 and -981.829924172.Subproblem 1
x + 1000 = 981.829924172 Simplifying x + 1000 = 981.829924172 Reorder the terms: 1000 + x = 981.829924172 Solving 1000 + x = 981.829924172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1000' to each side of the equation. 1000 + -1000 + x = 981.829924172 + -1000 Combine like terms: 1000 + -1000 = 0 0 + x = 981.829924172 + -1000 x = 981.829924172 + -1000 Combine like terms: 981.829924172 + -1000 = -18.170075828 x = -18.170075828 Simplifying x = -18.170075828Subproblem 2
x + 1000 = -981.829924172 Simplifying x + 1000 = -981.829924172 Reorder the terms: 1000 + x = -981.829924172 Solving 1000 + x = -981.829924172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1000' to each side of the equation. 1000 + -1000 + x = -981.829924172 + -1000 Combine like terms: 1000 + -1000 = 0 0 + x = -981.829924172 + -1000 x = -981.829924172 + -1000 Combine like terms: -981.829924172 + -1000 = -1981.829924172 x = -1981.829924172 Simplifying x = -1981.829924172Solution
The solution to the problem is based on the solutions from the subproblems. x = {-18.170075828, -1981.829924172}
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